The purpose of this project is development of the statistical theory for possibly misspecified stochastic regression models and their applications in assessing the association between disease and explanatory variables. The current research is focused on the effect of possible misspecification such as nonlinearity and/or heteroscedasticity on statistical properties of mean squared linear regression models. Theory has been developed that provides the asymptotic unconditional distribution of the least squares estimators of the regression coefficients in such models. The theory is being used to derive some new results in two applied areas. Firstly, to investigate the consequences of categorizing continuous explanatory variables as is routinely done in epidemiologic studies. The results have been presented at the ASA meeting and a paper is being prepared for publication. The second problem under investigation is assessing the effect of measurement errors in the explanatory variables and evaluating methods of adjusting for this effect. Theory has been developed for the case of general measurement errors that may have non-normal distribution, be heteroscedastic, and correlate among themselves and with the true values of the covariates, as is often encountered with self-reported variables such as nutritional intakes. The results of this work have been applied to evaluate statistical properties of different alternative energy adjustme models currently used in nutritional epidemiology. A paper on the effect of measurement error on inference for energy adjustment models has been conditionally accepted for publication.